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"What!? Obviously Doflamingo and any other New World saga antagonist can easily beat that Whitebeard pirate with the top hat whose name I forgot, the one who appeared for a few panels at Marineford. Also Barreltheif is my favorite poster on NF." - Eiichiro Oda (SBS)

Not at the beginning but he still got a good unexpected cut after he got serious and his men were surprised that Gokei was able to hang on so well thanks to his willpower
On the other hand Rinbukun was getting completely overwhelmed even when Tou purposefully took his blows head on (stated by Rokuomi) and got finished the very moment Tou decided to go for his head. Tou himself only suffered a very minor scratch

Even accounting for the different styles I don't think these fights should be in different tiers

That's the impression I had at first too, but upon rereading there's a moment, before the end, where one of the Duke's men says that it's time the Duke made his move. Then we've got a panel of him with a fierce expression slashing at Gokei, then he's got a little monologue before realizing that he has gotten slashed too. Then they proceed to fight for a moment, he finally pushes him back. The Wei soldier says that I Gokei gives up the duel and orders the troops to kill them the war will be won, he kills him instead and only them their last exchange happens
To me considering the injuries the Duke took it should be on the same tier as Rinbukun vs Tou but a bit higher, because Tou was doing the same thing as the Duke by taking Rinbukun's blows head on, was still overwhelming him, finished him as soon as he went for a decisive blow and made it out with a minor scratch not even as big as the one Renpa got avoiding (and not smashing @Crispy) the boulder in Sanyou